List of top Mathematics Questions on Permutation and Combination asked in NATA

What is the next number in the sequence? 2, 6, 12, 20, 30, ?

How many possible words can be created from the letters R, A, N, D (with repetition)?

A large newspaper is created using 100 sheets of paper folded in half. The pages are numbered from 1 to 400. A sheet is pulled out of the newspaper. If one of the page numbers on this sheet is 178, can you find out the numbers on the other three pages on this sheet of paper ?
(Marks will be awarded only if all 3 answers are right)
What four letter word can be written forward, backward or upside down and can still be read from left to right ? Provide the answer in capital letters.
Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. Then the total number of persons in the room is:
If a, b, c are odd positive integers, then number of integral solutions of a + b + c = 13, is
A class has n students, we have to form a team of the students including at least two students and also excluding at least two students. The number of ways of forming the team is
If \(^nc_7=^nc_4\), then the value of n is
\( m \) men and \( w \) women are to be seated in a row so that all women sit together. The number of ways in which they can be seated is: